Publisher Summary This chapter discusses the simple case of the turbulent boundary layer in a constant pressure field and considers the complex problem of the effects of pressure gradients, and variable wall roughness. The concepts of boundary layer phenomena, in general, and turbulent boundary layers, in particular, have found application in a wide range of fields including aeronautics, guided missiles, marine engineering, hydraulics, meteorology, oceanography, chemical engineering, atomic reactors, and the flow of liquids and gases in the human body. Many ideas for turbulent boundary layers involve assumptions other than those for turbulent shear stresses and in these cases, the validity of the results is examined first for laminar layers and then interpreted in the light of the possible shear stress patterns of turbulent layers. The effect of roughness on boundary layer characteristics is examined in the chapter. The wall is aerodynamically smooth for a turbulent boundary layer if the roughness elements are so small as to be buried in the laminar sublayer. Pressure gradients, Reynolds number, or roughness does not affect the constants of proportionality. The assumption of a constant outer viscosity has been investigated only for the case of equilibrium layers.